What is the distribution density function for a normal random variable?

Thread starter sampahmel
Start date Nov 13, 2008
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Distribution Normal Normal distribution

In summary, normal distribution is a statistical concept that describes a symmetrical bell-shaped curve commonly found in real-world data sets. It is important because it allows for predictions and serves as a basis for statistical tests and models. The characteristics of a normal distribution include symmetry, 68-95-99.7 rule, asymptotic shape, and the mean, median, and mode all being equal and located at the center. A standard normal distribution has a mean of 0 and a standard deviation of 1, making it easier for calculations and comparisons. Normal distribution is related to the central limit theorem, which states that the distribution of sample means will become more and more normal as sample size increases. This is why it is commonly used in statistical inference

Nov 13, 2008

sampahmel

I am confused with my homework problem in which it asked "If the random variable is normal, specify its distribution". What does it want?

sampahmel

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Nov 14, 2008

cronxeh

Gold Member

They want the distribution density function http://upload.wikimedia.org/math/6/0/5/605cea7cca0f8ae63e8b130b19aa60fd.png

What is normal distribution?

Normal distribution, also known as Gaussian distribution, is a statistical concept that describes a symmetrical bell-shaped curve. It is used to represent a set of data where the majority of the values cluster around the mean, and the rest of the values taper off symmetrically on both sides.

What are the characteristics of a normal distribution?

The characteristics of a normal distribution are:

It is symmetrical, with the mean, median, and mode all being equal.
About 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
The curve is asymptotic, meaning it approaches but never touches the x-axis.
The mean, median, and mode are all located at the center of the curve.

Why is normal distribution important?

Normal distribution is important because it is a common pattern found in many real-world data sets. It allows us to make predictions and draw conclusions about a population based on a sample, and it also serves as a basis for many statistical tests and models. It is also used in quality control, finance, and other fields.

What is the difference between a normal distribution and a standard normal distribution?

A normal distribution is any distribution that follows the characteristics of a normal curve. A standard normal distribution is a specific type of normal distribution with a mean of 0 and a standard deviation of 1. This allows for easier comparison and calculation of probabilities and percentiles.

How is normal distribution related to the central limit theorem?

The central limit theorem states that the sampling distribution of the sample means of a population will be approximately normally distributed, regardless of the underlying distribution of the population. This means that as the sample size increases, the distribution of sample means will become more and more normal. This is why normal distribution is often used in statistical inference and hypothesis testing.